Question: Multiply the following complex numbers: $({5-5i}) \cdot ({-4-2i})$
Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({5-5i}) \cdot ({-4-2i}) = $ $ ({5} \cdot {-4}) + ({5} \cdot {-2}i) + ({-5}i \cdot {-4}) + ({-5}i \cdot {-2}i) $ Then simplify the terms: $ (-20) + (-10i) + (20i) + (10 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ -20 + (-10 + 20)i + 10i^2 $ After we plug in $i^2 = -1$ , the result becomes $ -20 + (-10 + 20)i - 10 $ The result is simplified: $ (-20 - 10) + (10i) = -30+10i $